I am looking for textbooks on math contests that give the theory associated with the topics (such as graph theory,geometry,Trig,combinatorics,etc) before giving a large volley of problems to solve(apart from AoPs). I am a high schooler and complete beginner to these. Is there a textbook that discusses theory as good as Arthur Engel has done for problem solving in the book Problem Solving Strategies?
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$\begingroup$Here are the books I recommend every mathlete from my personal experience:
Geometry and Trigonometry:
- Euclidean Geometry in Mathematical Olympiads by Evan Chen: This is the most recommended book for Olympiad geometry. The book goes through many important concepts and also gives insights of solving problems.
- Geometry Revisited by H.S.M Coxeter: An awesome classic. Some IMO medalists still recommend this book above EGMO.
- Geometry Unbound by Kiran S. Kedlaya: If you've completed all necessary concepts in geometry and want to solve some good problems, this is the book you're looking for.
- 103 Trigonometry Problems by Titu Andreescu: A good problem book for Olympiad trigonometry.
Inequalities:
- Secrets in Inequalities volume 1 and 2 by Pham Kim Hung: The best inequality book. But not recommended for a complete beginner as the problems here are very high level.
- Inequalities a Mathematical Olympiad Approach by Rogelio: A good book for Olympiad inequalities. Also suitable for beginners.
- Inequalities- Theorems, Techniques and Selected Problems by Cvetcovski (suggested by Dr. Mathva)
- Inequalities an Approach Through Problems by B J Venkatachala
Functional Equations:
- Functional Equations and How to Solve Them by Christopher G. Small
- Functional Equations a Problem Solving Approach by B J Venkatachala
Algebra:
- 101 Problems in Algebra by Titu Andreescu
Number Theory:
Modern Olympiad Number Theory by Aditya Khurmi (suggested by Dr. Mathva)
Olympiad Number Theory Through Challenging Problems by Justin Stevens
Number Theory a Problem Solving Approach by Titu Andreescu
104 Number Theory Problems by Titu Andreescu
Combinatorics:
- A Path to Combinatorics for Undergraduates by Titu Andreescu
- 102 Combinatorial Problems by Titu Andreescu
- Problem Solving Methods in Combinatorics by Pablo Soberón
- Graph Theory by Xiong Bin
Problem Solving:
- The Arts and Crafts of Problem Solving by Paul Zeitz: The best problem solving book. Also a good resource for recreational mathematics problems.
- How to Solve It by George Polya.
Again, I mention these are my recommendations. Others suggestion may differ from this (you may add your suggestions in the comments). And there might be some books I forgot to include. May your math journey be enjoyable. Happy problem solving!
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